Estimating the redshift error in supernova data analysis

Recent works have shown that small shifts in redshift -- gravitational redshift or systematic errors -- could potentially cause a significant bias in the estimation of cosmological parameters. I aim to verify whether a theoretical correction on redshift is sufficient to ease the tension between the estimates of cosmological parameters from SNe 1a dataset and Planck 2015 results. A free parameter for redshift shift($Δz$) is implemented in the Maximum Likelihood Estimator. Redshift error was estimated from the Joint Light-curve Analysis(JLA) dataset and results from the Planck 2015 survey. The estimation from JLA dataset alone gives a best fit value of $Ω_m = 0.272$, $Ω_Λ = 0.390$, and $Δz = 3.77 \times 10^{-4}$. The best fit values of both $Ω_m$ and $Ω_Λ$ disagrees heavily with results from other observations. Information criteria and observed density contrasts suggest that the current data from SNe 1a is not accurate enough to give a proper estimate of $Δz$. A joint analysis with Planck results seems to give a more plausible value of the redshift error, and can potentially be used as a probe to measure our local gravitational environment. 7 pages